Parallel projection can be regarded as a special case of central projection in which the centre of projection is an infinitely distant point.


 In asking about the point of this, one is tempted to expand the question in order to ponder the point of anything at all. A pointless pursuit, you say? Well yes, and yet one might point out that there is a point reached in every thinker's career when one confronts the question of basic meaning point-blank, as it were. This, of course, does not necessarily engender a sharpening of the wit or that gift for making the pointed remark so assiduously cultivated by the smart set. Nor does it tend to enhance one's ability to score points in the endlessly absorbing contest of social gamesmanship. As a matter of fact, persons having reached the point of bewilderment appear abstracted, confused and lost, as though they could use a compass to point their way out of the puzzlement. A new tack, a fresh point of view perhaps? Not their strong point, you say? One can advise forgetting the whole problem, but it may be pointed out that at the point of death the point in question will inevitably assert itself and one might just as well tackle it, sit down on the old needle-point, and focus the mind on an infinitely distant and invisible point. What's the point of that, you say? Ah yes ... it does seem that we have come full circle back to the starting-point.

 Origin, unity, the centre. . . . That is what the point symbolizes. It represents the principles of emanation and manifestation and it is that around which everything revolves. Alone and unmoved, it contains the totality of all possibilities and the human mind constantly intuits its primacy. Every phrase admonishing one to stick to the point, get back to the main point, or make a point of doing something contains within it an underlying awareness of a seminal core to things which is unvarying and original. Somehow the simplest mind apprehends that all lines which terminate in the circumference of a circle begin from a central point, and that any set of circumstances can be traced back to some such cause. This is true even at the most relative level and is consciously experienced by whole societies of human beings who perceive reality in relation to certain meaningful principles which rest at the very heart of their collective enterprise. Ortega y Gasset expressed this neatly when he wrote that "the choice of a point of view is the initial act of a culture".

 The point at the centre of all things is sacred because it remains unmoved and because it is an axis which links the unmanifest with the manifest. In one way or another, thinkers from all cultures have conceived of that archetypal point as the Pivot of the Law, the basis of interaction between the three worlds. The outbreathing and inbreathing of the universe and all the centrifugal and centripetal action in phenomenal nature can be traced back ultimately to it. Everything emerges from it, revolves around it and returns to it, and it or one of its myriad progeny will be the reference point that lends order and meaning to all patterns of change in the world. It is because of this axis, this zero point, that man possesses any sense of time or space. Without a glimmering awareness of a still point within him and within the universe surrounding him, man would not experience a conscious sense of direction or of sequence. Like an animal, he would feel and act in accordance with the Law as it expresses itself through his nature: unquestioned, unexamined, unfettered by any conscious design. Instead, man orients his beliefs and his sense of order to some sort of pole-star. He departs in action from a point of beginning and returns to that point repeatedly in his efforts to understand the direction of his movement. The human mind thus charts its course, and an inevitable expression of this continual tendency can be found in the invention of the pivotal compass, whose magnetic needle is freely suspended at its central point of gravity. This instrument acts as a linking mechanism between man and the vast physical world around him, for, though he can use his movable sight to establish his own relative bearing, the needle will align itself to the total magnetic field vector and establish his position relative to the polar point.

 There are two kinds of points; that which has no magnitude at all, which is metaphysical, and that which has the smallest conceivable magnitude and is manifest. The latter is a point in time and space, whilst the unmanifest answers to what the Hindus call 'the point beyond time', or Pure Being, in the language of the Taoists. Though incomprehensible to the finite mind, it is the point of equilibrium and harmony at the centre of the phenomenal universe. The Hebrews called it Shekinah, the central presence of God, and in the Islamic tradition it is revered as the Divine Abode, the eye of the Heart. The idea of this point provides the basis upon which is formulated all notions we have regarding degree. In the words of Moses de Leon, "This degree is the sum total of all subsequent mirrors, that is, of all external aspects related to this one degree. They proceed therefrom because of the mystery of the point, which is itself an occult degree emanating from the mystery of the pure and awe-inspiring ether. The first degree of all is absolutely occult, that is, not manifest, and cannot be attained."

 The problem of understanding the relation between the One Point and the many has fascinated philosophers for millennia. This becomes particularly absorbing when the point is viewed as a symbol of unity and, therefore, the Good. Proclus observed that "The more complete is the cause of more, in proportion to the degree of its completeness: for the more complete participates in the Good more fully ... it is nearer to the Good . . . the cause of all." This implies that the closer one moves towards the metaphysical, central point of existence, the greater the ability to act as a channel for the Good. But where is that centre and how does an individual recognize it in time and space?

 Peasants all over the world intuitively recognize its presence in the seed they plant in the earth. The Hopi tenderly handle the maize seed in their hands and speak to the spirit within it whilst placing it in the soil. They recognize a point of immortality within the seed, a germ which never dies through all the cycles of sowing and reaping. They handle thousands of seeds and yet they salute this one same germinal spirit in each. Perhaps they intuit the relation between the One Point and the many. Artists also may sense something concerning this in their perception of the light inherent in each daub of paint. Neo-Impressionists and Pointillists developed this idea to a high degree. Painters like Georges Seurat displayed an unerring sense of relationship between tones, intervals and accents on the basis of individual points containing varying degrees of white mixed with colour. Seurat was fascinated with the study of space, perspective, light and the sensation of air moving around objects. Each point in his complex canvases contains within it the capability of expressing these elements, but it is only together as a whole pattern that they are able to manifest them clearly. It is when viewing the mass of points from a proper distance that one can grasp the more general point of the painting as envisioned by its creator.

 Inspired by the ideas of the Pythagoreans and neo-Platonists, Renaissance thinkers paid homage in poetry and prose to the symbolism of the point. They echoed the ancient observance regarding the circle, which was said to have its circumference nowhere and its central point everywhere. Some, like Pelletier, recognized that "Unity, which represents the Point in geometry, is not Number, but only the origin of number." These two ideas allude to the mystery that shrouds the One Point which stands at the threshold dividing the noumenal and phenomenal planes. On a more commonplace level, a typical definition of the point goes back to Euclid, who declared that it was that which had no parts. This sort of mathematical definition asserts nothing about the existence or non-existence of the thing defined. It only suggests that it is possible to have an intuition of what a thing is and that its existence can be proved when it is shown why it exists by means of a construction. The essence of the point was never questioned by Euclid nor by Aristotle. They did not consider the point to be a reflection of an ideal or an eternal paradigm, nor did they attempt to take their analysis beyond assertion or proof to discover how the ultimate principles of the One and the Dyad account for points and lines and other figures.

 To see a solid body in a point must have its ground in a point, which has no point, if one thinks it over.


 With certain refinements in thinking linked to a less mechanical view of nature, more recent mathematicians tend to view the point as the minima visibilia, supposing an infinitely fine vision. One imagines an infinite division of the atom, perhaps, and that congruence is the intuitive connection of their couples. The singular point is the one expression that is always present in all systems of geometry. "While primitive relations vary, the fundamental terms, namely points, remain always the same." Points would seem thus to be the one indispensable element of geometry, and yet one may ask if they are closer to nature than volumes. Is our perception of points only possible when they are big enough to be seen, or must we predicate a paradigmatic realm where the question of volume does not arise? When does the geometry of points become that of volumes, or are they translatable? In an ideal realm, is substance homogeneity or is there a subtle heterogeneity involving points and breadth and depth?

 In the phenomenal and highly heterogeneous world there are regular systems of points observable in the arrangements of atoms and molecules. Crystallography reveals a good deal about the regularity of point patterns in nature. A salt crystal can be described as a cubic lattice with its points occupied alternately by a chlorine atom and a sodium atom. Each of its lattice points has six neighbouring points, unlike the diamond which exemplifies the tetrahedral lattice, or other molecular structures consisting of several congruent interlocking lattices. The regularity of pattern is consistent and suggests an essentially unchanging quality in the points. It might be asserted that the regularity is possible because of the one-pointed intelligence within the atom which, clothed in a subtly differentiated aspect of nature, is limited to the expression of this oneness in the guise of a singular and regular pattern. This would answer to the notion of congruence as the intuitive connection of points and to the idea that the One Point contains all potential points and gives meaning to the phenomenal points which then act in the likeness of the original.

 In differential geometry it may happen that the curvature of a surface has the same value for all normal sections at a point. When this occurs, the principal directions are said to be indeterminate and the point is referred to as an umbilical point. A surface consisting entirely of umbilical points is also one in which all plane sections are circles composing what we readily recognize as a sphere. In general, the umbilical points of a surface are isolated and the net of lines of curvature may have singular properties at these points only. When the point of a surface assumes all the positions possible on the surface, then the two foci on its normal tend to take on all possible positions on a certain pair of surfaces which are jointly called the evolute or surface of centres of the original surface. In the case of a sphere, the evolute consists of the centre of the sphere alone, since all foci are at this point. Because of this, "the sphere is the only surface for which one sheet of the surface of centres degenerates into a point". Very simply put, a sphere is a "class of points separated from a certain point by a constant distance" and it is also the form which mirrors most perfectly what we intuitively identify as the essential point itself. A surface entirely composed of umbilical points, each of which could become the evolute of myriad generations of spheres, lays the basis for an infinite involution of the principle of the One Point in matter. It can be said that in the universe geometry is integrally embodied in the first view met. Its points are the elementary data of this view and its congruence is the connection of couples of this data. "Then it is embodied again in each one of the following views, successively taking for points and congruence the elementary data of each view and the connection of their couples."

 Infinite love must fill all Eternity as the omnipresence of God and yet it must be infinitely expressed in the smallest moment by enabling one to see in every moment that which is in all. ... It is both ways infinite, for my soul is an infinite sphere at the centre.


 The One Point in space and time is poetically grasped by many sensitive individuals, and yet some, like Dante, have frozen the notion in focussing upon the marvels of a fixed sphere with a central point revealed only at the finish of the journey. This is to look at the idea of the One Point objectively, from the standpoint of the individual pilgrim who is somehow separated from that point in space and time. If one considers the more essential character of the point in itself, it seems to transcend objectivization.

 After all, the point has no direction but contains in itself all possible directions. It represents an infinite possibility for action, and in this regard is the perfect symbol of freedom, whilst at the same time remaining a focus of concentration in the midst of the indefinite diffusion of space. "The point wills and wills itself." In space and time there is no fixed point. The moment passes with the circling of the wheel of duration. But the actor can participate in the action of samsara whilst focussing upon a pivotal reality which rests at the centre of the manifest sphere. Metaphysically, it is only because this point exists eternally that all other points are aligned in a circle and there is duration rather than a confused anarchy of moments. Each moment is in relation to others but takes meaning in relation to that which is changeless, eternal and mysteriously outside all others. In this sense it can be said that each moment is in time but also outside of time . . . animated by a non-temporal power.

 Leibniz observed that external things present the property of extension to our senses only. This extension of parts takes place in terms of plurality (number), continuity (with time and motion) and coexistence (with non-extended things). Anything continuous is infinitely divisible; there is no end to number, time or motion in this sense. Only that which is truly eternal is neither composite nor has its subsistence in something else. If atoms are divided ad inpnitum, they become reduced to mathematical points which would seem to lead to a loss of their extension. Leibniz perceived, however, that their inner life suggested an infinite extension in the metaphysical direction (dimension) where the real essence of what appears in space as a mathematical point can be grasped. In the words of The Secret Doctrine, Occultism draws a line between "the absolutely Ideal Universe and the invisible though manifested Kosmos. Our Gods and Monads are not the Elements of extension itself, but only those of the invisible Reality which is the basis of the manifested Kosmos." Thus, every physical point in the universe is but the phenomenal expression of the noumenal Point, whilst the gods and Monads represent unique and ontologically superior expressions of it. Atoms are divisible and extendable, whereas every Monad is a living mirror of the universe. Leibniz said that anything capable of extension must necessarily contain at least two points, an assertion which recognizes that it is not the point itself which is extended.

 Plato, following the Pythagorean teachings, frequently referred to cosmology in terms of points (fire), lines (water), superfices (air) and solids (earth). This sequence clearly indicates the conceptual and ontological gap existing between the point and volume, and it lays the basis for understanding how ideation can be expressed in concrete terms. As an aid to this conceptualization, Plato described a point as an extremity of a line, a line as an extremity of a surface, and a surface as an extremity of a solid. Thus the line surpasses a point by one dimension (length), a superfices by two (length and breadth), and a solid by three (length, breadth and depth). These dimensions involve number, which Pythagoras defined as the "extension and energy of the spermatic reasons contained in the Monad". This unity or Monad is the very principle of interval and dimension, but is itself capacious of neither of these conditions. It is the Mother of All Numbers, which the Pythagoreans referred to as Lethe or oblivion, the Rigid Virgin or Atlas who is an ineffable support, connecting and separating all things. They spoke of the Ineffable One of which the Monad is an image and distinguished between it as the cause of all unity and measure, theαπÎιρoυ, the infinite " cause of all unity and the measure of all things", and the Duad, which is the divisible mother substance.

 The point that merges back into the 'circle' after emanating the first three points and connecting them with lines thus forms the first noumena! basis of the Second Triangle in the manifest world. The apex of this triangle is the Monad or Father, the left line the Mother, and the right line the Son. The base line demarcates the universal plane of productive nature and divides the triadic cap in the Pythagorean Decad from the seven points below it. The Pythagoreans saw the monadic apex of this emanation in terms of pure ideation. They attributed scientific knowledge to the duad, opinion to the triad, and sensory perception to the tetrad, thus paralleling the procession of point, line, superfices and solids, which is descriptive of the manifest cosmos. In every such procession the monadic point remains the principle of unchanging unity which determines the relationship of members to each other and to the whole. It is the pivotal point of the Law governing that system, all parts of which behave in a dependent and regular manner. This is because emanation persists during an entire cycle of evolution, and only at the end of that cycle will emanation itself be drawn back into the One Absolute.

 In his De Dignitate, Pico della Mirandola asserted that man is like a point and a centre to which all parts of the world are related. Man is a point destined to become a circle and to expand is to realize one's potential humanity. In German philosophical thought, from Boehme to Schelling, the entire scheme of life is an unfolding, from a point, of an enveloped God. This they saw as divine expansion and contraction which is mirrored in the procession of human intellection where all interior energy appears in immediate consciousness as a concentrated focus previously disseminated elsewhere in a point. This mental contraction then yields to the broader unity inherent in the more archetypal point by diffusing its energy outward, only to be followed once again by subsequent contraction and expansion. The fundamental image of the autonomy of the mind in consciousness is thus one of a geometric point which eternally formulates and maintains itself. The German philosopher Fichte related the concept of freedom to this image, saying that it "can only be conceived formally as a concentration of the flowing plurality of virtual light on a central point, and as the diffusion of light, from this central point, in a multiplicity that is sustained and lit only in this way". In contemplating the notion of freedom in relation to the One and the many, a progressive transcendence of objectivity is suggested. Seers who are especially trained can conceive of an indivisible unit without slipping into an annihilation of the idea with its subject. They can 'see' the pure dual light of spirit and nature in one.

 They see the Real in the unreal, the noetic in the psychic, the noumenal in the phenomenal. In attempting to illustrate this relationship, H.P. Blavatsky wrote, "As a cone stands on its point, or a perpendicular straight line cuts a horizontal plane only in one mathematical point, but may extend infinitely in height and depth, so the essences of things real have only a punctual existence in this physical world of space; but have an infinite depth of inner life in the metaphysical world of thought." This point is one of perfect equilibrium, a zero point or laya state where substance becomes homogeneous and is unable to act or differentiate. Though in a neutral condition to the manifest world, such a point is the Central Spiritual Sun, the ever-emitting life-centre of the cosmos. It is the umbilical point echoed in differential geometry on the phenomenal plane and symbolized in the beautiful myth of Maha Vishnu, from whose navel the lotus containing the universe arose. Floating upon the waters of endless Space, the great Supporter of all the universes contains the ever-concealed Germ capable of emanating forth in a thousand-petalled perfection perceived in every point of time and space by Masters of Wisdom.

 This umbilical or zero point is aptly described by the term bindhu, which, whilst simply meaning 'point' or 'spot', also refers to an apparently insignificant incident, the effects of which spread like a drop of oil on water. In the Hindu tradition it is the esoteric term for point, the centre of a mandala and the limit of manifestation. When something exists yet does not exist, it is represented by a bindhu, and at the great dissolution of the universe, all is reabsorbed into the bindhu. In meditation the mind focusses upon the bindhu as the realization of cosmic energy, and when it is worn as a spot on the forehead, it is an affirmation of the role of Shakti. Women entering the grihastha stage thus align themselves to the sacred source of creative energy by centering the bindhu spot at the place of the Third Eye.

 This spot is a meaningful progeny of the One Point that arose in the immaculate white disk at the dawn of differentiation. Out of this Divine Unity the Ray of the Ever Darkness flashes into the Germ-Point which is matter in the abstract and which ultimately exists in the centre of every subsequent manifest atom. The Circle with one central Point is parentless and numberless. It is Anupadaka and can fall under no calculation. The Point generates the line which represents the Androgynous Logos. When the triad emerges, the Son of the Father fructifies the Virgin matrix of Kosmos, who then gives birth to that form which combines all forms. Thus the progeny of Primordial Light and Chaos is the Central Spiritual Sun, itself a mirror of the Invisible Point from which the Ray was first emitted. According to Hermes Trismegistus, "the point within the circle, was not yet the Architect, but the cause of that Architect; and the latter stood to it in precisely the same relation as the point itself stood to the circumference of the Circle [the immaculate white disk] which cannot be defined". This is what is meant by saying that Parabrahmam cannot be known except through the luminous Point of the Logos which Itself knows only Mulaprakriti, the veil upon Parabrahmam.

 This Light of the Logoic Point pervades the universe, and through the Divine Will of the Architects gives birth to every form. From it springs the endless chain of interaction between spirit and matter, giving rise to all chemical action, all molecular structures, all natural forms. The sun is a focus for this on the physical plane, "the lens by which the rays of the primordial Light become materialized", and within every cell of organic life a Monadic synthesis of its essence resides. It is the Germ-Point which is everywhere, the Unmanifest in all manifest forms. Only the focussed concentration of the totally centered human mind is capable of bathing self-consciously in that Light, and to achieve such transcendent one-pointedness requires a deliberate negation of all that is divisible and extended. To make of oneself a zero means to have realized the indivisible, unchanging neutral point within which is the aperture, as it were, opening to the unmanifest potency of the One Eternal Source. At this point the drop may merge with the ocean, the beautiful thousand-petalled lotus with its seed. The world, turning around its still Point, may cease to exist and the vortices of all past and future worlds sigh as they fold in upon themselves in one diminishing bindhu. The Eye of Lord Shiva closes and Maha Vishnu slumbers at one with the Endless Deep. The point is everywhere, without circumference. Everywhere and nowhere, the same.

From any point

A line reaches back

And attaches to a far distant centre.

There is no unconnected life in this world,

Nor a point in time

Unknown by any other point.

Nor a tear shed in a vacuum.